Asynchronous Spiking Neural P Systems with Local Synchronization Tao Song 1 , Linqiang Pan 1 , Gheorghe P˘aun 2 1 Key Laboratory of Image Processing and Intelligent Control Department of Control Science and Engineering Huazhong University of Science and Technology Wuhan 430074, Hubei, China lqpan@mail.hust.edu.cn 2 Institute of Mathematics of the Romanian Academy PO Box 1-764, 014700 Bucure¸ sti, Romania, and Department of Computer Science and Artificial Intelligence University of Sevilla Avda. Reina Mercedes s/n, 41012 Sevilla, Spain gpaun@us.es Summary. Spiking neural P systems (SN P systems, for short) are a class of distributed parallel computing devices inspired from the way neurons communicate by means of spikes. Asynchronous SN P systems are non-synchronized systems, where the use of spik- ing rules (even if they are enabled by the contents of neurons) is not obligatory. In this paper, with a biological inspiration (in order to achieve some specific biological func- tioning, neurons from the same functioning motif or community work synchronously to cooperate with each other), we introduce the notion of local synchronization into asyn- chronous SN P systems. The computation power of asynchronous SN P systems with local synchronization is investigated. Such systems consisting of general neurons (resp. unbounded neurons) and using standard spiking rules are proved to be universal. Asyn- chronous SN P systems with local synchronization consisting of bounded neurons and using standard spiking rules characterize the semilinear sets of natural numbers. These results show that the local synchronization is useful, it provides some “programming capacity” useful for achieving a desired computational power. 1 Introduction Membrane computing is one of the recent branches of natural computing. It was initiated in [9] and has developed rapidly (already in 2003, ISI considered mem- brane computing as a “fast emerging research area in computer science”, see http://esi-topics.com). The aim is to abstract computing ideas (data struc- tures, operations with data, ways to control operations, computing models, etc.) from the structure and the functioning of a single cell and from complexes of